Case Assignment: The Following Table Gives Short Run And Lon

Case Assignmentthe Following Table Gives Short Run And Long Run Total

The following table gives short-run and long-run total costs for various levels of output for a perfectly competitive firm: Output (Q), SRTC, AVC, TR. Note: AVC is Average Variable Cost, TR is Total Revenue, SRTC is Short Run Total Cost. The formulas are as follows: SRTC = FC + VC, and Total Cost = Fixed Cost + Variable Costs. The fixed cost (FC) of production is $350 and the price (P) is $55. Complete the table based on this information. For output levels Q=2 and Q=3, determine the marginal cost. Using the market price of $55, identify the profit-maximizing output level for the firm. Calculate the resulting profit or loss at this level. Also, analyze whether the firm should shut down in the short run when experiencing a loss, and explain your reasoning.

Paper For Above instruction

In a perfectly competitive market, firms face a highly simplified yet effective decision-making process based on cost structures and market prices. The firm aims to maximize profit, which occurs at the production level where marginal revenue equals marginal cost. Given the data provided and the fixed cost of $350 alongside the market price of $55, this paper analyzes the optimal production decisions, profit or loss calculations, and shutdown considerations for the firm.

Completing the Cost Table

The initial step involves completing the table with the missing values—specifically the short-run total cost (SRTC), average variable cost (AVC), and total revenue (TR) at various output levels. Since SRTC = FC + VC, and FC is $350, the variable costs (VC) can be derived from AVC, which is defined as VC divided by Q. The formulas guide us to systematically fill in the data as follows.

Suppose at each output level Q, the variable cost VC is calculated as AVC times Q, and SRTC as FC plus VC. Total revenue is computed as price P (which is $55) times Q. For instance, at Q=2, if AVC is known, VC = AVC * 2, and SRTC = 350 + VC. The table is then populated accordingly, ensuring coherence with the formulas and the data provided.

Calculating Marginal Cost at Q=2 and Q=3

Marginal cost (MC) is the additional cost incurred from producing one additional unit of output, calculated as the change in total cost divided by the change in quantity: MC = ΔSRTC / ΔQ. For Q=2 to Q=3, the calculation involves the SRTC values at these two output levels. For example, if SRTC at Q=2 is $450 and at Q=3 is $505, then MC = ($505 - $450) / (3 - 2) = $55. This process is repeated to find the marginal cost between Q=2 and Q=3.

Determining the Profit-Maximizing Output

In perfect competition, the firm maximizes profits where marginal cost equals marginal revenue (the market price). Since the price P is $55, the firm will produce at the output level where MC approximately equals $55, considering the discrete output data points. This involves reviewing the calculated MCs across different levels of Q from the completed table. The optimal Q is the one where MC ≤ P, but producing one more unit would push MC above P, reducing profit.

Calculating Profit or Loss at the Optimal Output

Profit is computed as total revenue minus total cost: Profit = TR - SRTC. After selecting the profit-maximizing Q based on MC and P, plug in TR and SRTC values at that Q to determine the profit or loss. A positive result indicates profit; a negative value indicates loss.

Should the Firm Shut Down in the Short Run When Experiencing Loss?

The decision depends on whether the firm's revenue at least covers variable costs. If TR is less than the total variable costs (VC), then the firm should shut down temporarily because continuing production would increase losses beyond fixed costs. However, if TR covers variable costs but not total costs, the firm should continue operating in the short run, as it can at least contribute towards fixed costs, minimizing total losses. This principle is rooted in the shutdown rule, which suggests that a firm should shut down if P

Conclusion

In conclusion, completing the cost table with the data provided enables firms to analyze their cost structures effectively. By calculating the marginal costs at key production levels and comparing these to the market price, firms can determine their optimal output. Understanding the shutdown rule informs whether a firm should cease production temporarily to minimize losses when facing short-term losses. This decision-making process hinges on accurate cost and revenue data, illustrating the importance of comprehensive cost analysis in firm strategies within perfectly competitive markets. Further research into market dynamics and cost behaviors can better equip firms to make informed production and shutdown choices, ultimately enhancing their profitability and sustainability.

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